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2007, Volume 7, Issue 4: 779-792. Doi: 10.3934/dcdsb.2007.7.779
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Circular and elliptic orbits in a feedback-mediated chemostat

  • 1.

    Department of Mathematics, University of Florida, Gainesville, FL 32611-8105

Received:  July 31, 2006
Revised:  December 31, 2006
Published:  October 2007
Abstract Related Papers Cited by
    Abstract
  • A chemostat with two organisms competing for a single growth-limiting nutrient controlled by feedback-mediated dilution rate is analyzed. A specific feedback function is constructed which yields circular and elliptical periodic orbits for the limiting system. A theorem on the stabilization of periodic orbits in conservative systems is developed and for a given elliptical orbit, the result is used to modify the chemostat so that the chosen orbit is asymptotically stable. Finally, the feedback function is modified so that finitely many nested periodic orbits of alternating stability exist.
    Mathematics Subject Classification: 92D25, 92D37, 92D45.

    Citation:
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